interjection similar in meaning to fooled you! or gotcha! after a prank. It first appeared in the tv sitcom The Big Bang Theory and is used by the character named Sheldon.
It probably comes from the word zing and ba and a may just have been added for added effect. See video of Bazinga!-moments

(Ancient Greek) frog . Features in Aristophanes'comedy Batrachoi ("The Frogs", (405 BCE) - as translated by Matthew Dillon. The phrase was also used by Hans Christian Andersen, in the fairy tale Tommeliden ("Thumbelina", 1835)

a shrill humming sound, such as from a bullet or vibrating string. As a verb: to move very quickly, especially while making a high pitched sound. As a noun used figuratively, meaning zest, vitality, or (in cuisine) spicy flavor. In comedy, zing is sometimes used as an interjection to acknowledge a witty comeback. The witty comeback itself is then called a zinger.